MOYAL FORMULATION OF QUANTUM-MECHANICS

This is a review paper on the formulation of nonrelativistic Quantum M echanics on Phase Space. In an overlook to the traditional approach, w e present the basic concepts including the Weyl mapping, the Wigner fu nction, the Moyal propagator and the Spectral projections. We discuss the advantages and the disadvantages of this formulation. We apply it to the study of quadratic Hamiltonians. The Stratonovich-Weyl correspo ndence is presented as the natural framework in which the theory can b e extended to include spin, relativity and constraints. The theory of identical particles is also considered.